Lexicogrammar is not a word you hear much but those of a certain following – cognitive linguists, functional grammarians, etc – use this word to describe what is traditionally call vocabulary and grammar as one system rather than being two separate systems.
As a researcher in prepositions this is a big deal. It means I (can) treat prepositions as vocabulary, requiring them to be learnt by students when before they were and still are somewhat relegated to the category of grammar. Vocabulary and grammar should not be studied separately. Vocabulary are not individual words to be studied, or looked up when you don’t know the word. Vocabulary only have full function within a sentence, and shine bright within the context of use within communication. Certainly, in Saussurean linguistics the signifier/signified duality of words are an important and enlightening feature. But words are best understood in communicative units, namely sentences. And Saussure will not have argued against that. In fact he argued for it.
Undoubtedly dictionaries are useful tools. But they generally push the learner to think of words as separate objects with separate meanings. Good dictionaries will give plenty of examples of usage but students will generally use the cheapest or most handy dictionary at hand. Today this is the smartphone dictionary and translator. Rarely do they give examples. And for most of the time they give one translation to one word, suppressing the multiple nuanced (often schematically-related) meanings that most words have. I shall talk about this point in another post.